Dynamic spatial theory has been a fruitful approach to understanding economic phenomena involving time and space. However, several central questions still remain unresolved in this field. The identification of the social optimal allocation of economic activity across time and space is particularly problematic, not been ensured yet in economic growth. Developing a monotone method, we study the optimal solution of the spatial Ramsey model. Under fairly general assumptions, we prove the existence of unique social optimum. Considering a numerical implementation of our algorithm, we study the role played by capital mobility in the neoclassical growth environment. With capital irreversibility and economic openness, space allows for transitional dynamics. Moreover, in this context, capital mobility is beneficial as well in terms of social welfare and inequality. We also consider an application of our method to an extension of the spatial Ramsey model for optimal land-use planning.

We analyze the spatio-temporal dynamics of a simple model of macroeconomic geography in which demography and pollution dynamics mutually affect each other. Pollution, by reducing the carrying capacity of the natural environment – which determines the maximum amount of people a given location can effectively bear – crucially affects labor force dynamics which in turn alter the amount of resources available for abatement activities aiming to reduce pollution. Such mutual links determine the eventual sustainability of the development process in different locations and economies, and spatial interactions further complicate the picture. We show that neglecting the existence of mutual feedback between population and pollution leads to misleading conclusions about the eventual sustainability of a specific location. We also show that even neglecting the existence of spatial externalities can lead to misleading conclusions about the sustainability of different regions in the spatial economy. This suggests thus that both the nature of the population and pollution relationship and geographical factors may play a critical role in the process of sustainable development.

There is little information published on patch expansion of perennial weeds and none for Apocynum cannabinum. Studies were conducted to measure the between-season and in-season expansion patterns of natural A. cannabinum patches over three growing seasons. Regression analysis indicated strong relations between patch area in consecutive years 1996 to 1997 (r 2 = 0.81) and 1997 to 1998 (r 2 = 0.76). Patches less than 20 m2 in 1996 increased in area by more than 100% in 1997 during a fallow season. However, patches decreased in size 6 to 51% between 1997 and 1998 when Glycine max was grown. Evidence suggested that a late-season mowing of the A. cannabinum patches in 1997 contributed more to the decline in patch area than competition from G. max during the 1998 season. The relations between patch area and growing degree units (r 2 = 0.97) indicated that greater than 89% of the terminal patch expansion occurred prior to the accumulation of 435 growing degree units (GDU) (June 19, 1997; May 31, 1998; June 9, 30-yr average), with minimal patch expansion between 435 and 1,000 GDU. Patches were at 50% of their final area on May 27, 1997, and May 14, 1998, a time when only 22% of the A. cannabinum population had emerged (r 2 = 0.99). Knowledge of patch size and expansion could help growers time weed scouting, to account for the later emergence patterns of this species, as well as assist in timing appropriate weed management efforts. This information could also be used in conjunction with aerial photographs to project potential patch size for site-specific management of this weed.

Combine harvesters have the potential to disperse weed seeds great distances. Reducing this dispersal may be important in an integrated weed management system. The objectives of this study were to determine the distance that wild oat seeds are dispersed by a combine harvester and the effect of chaff collection on combine harvester seed dispersal. This was measured by sampling wild oat seeds at varying distances behind a combine equipped with a removable chaff collection system after it passed through a wild oat patch. Chaff collection consistently reduced the amount and distance that wild oat seeds were dispersed. This occurred because more than 74% of the total wild oat seed that were ejected from the combine were in the chaff. Because most of the chaff falls in a row directly behind the combine, chaff collection only affected dispersal in this area. In 1996, chaff collection reduced wild oat seed dispersal past the wild oat patch to less than 10 seeds m−2 at 45 m, whereas without chaff collection, there was greater than 10 seeds m−2 up to 145 m. At distances beyond 145 m, chaff collection had no significant effect on seed dispersal. Chaff collection may be an important tool in an integrated weed management program because it may slow weed invasions and reduce the expansion of weed patches.

Comparing distributions among fields, species, and management practices will help us understand the spatial dynamics of weed seed banks, but analyzing observational data requires nontraditional statistical methods. We used cluster analysis and classification and regression tree analysis (CART) to investigate factors that influence spatial distributions of seed banks. CART is a method for developing predictive models, but it is also used to explain variation in a response variable from a set of possible explanatory variables. With cluster analysis, we identified patterns of variation with direction of the distance over which seed bank density was correlated (range of spatial dependence) with single-species seed banks in corn. Then we predicted patterns of the seed banks with CART using field and species characteristics and seed bank density as explanatory variables. Patterns differed by magnitude of variation in the range of spatial dependence (strength of anisotropy) and direction of the maximum range. Density and type of irrigation explained the most variation in pattern. Long ranges were associated with large seed banks and stronger anisotropy with furrow than center pivot irrigation. Pattern was also explained by seed size and longevity, characteristics for natural dispersal, species, soil texture, and whether the weed was a grass or broadleaf. Significance of these factors depended on density or type of irrigation, and some patterns were predicted for more than one combination of factors. Dispersal was identified as a primary process of spatial dynamics and pattern varied for seed spread by tillage, wind, or natural dispersal. However, demographic characteristics and density were more important in this research than in previous research. Impact of these factors may have been clearer because interactions were modeled. Lack of data will be the greatest obstacle to using comparative studies and CART to understand the spatial dynamics of weed seed banks.

A model is presented of the spread of a weed from a point source, with dispersal being both unaided and aided by a combine harvester. Four “type” weeds were modeled, chosen to represent species of differing population and dispersal ecologies and based broadly on Avena spp. (wild oats), Raphanus raphanistrum (wild radish), Bromus spp. (bromegrass), and Fumaria spp. (fumitory). Wind-adapted species were excluded. The greatest rate of spread was predicted to be for R. raphanistrum and the least for Fumaria, regardless of whether dispersal by combine harvester was included. Rate of spread was more sensitive to dispersal parameters than to demographic parameters and increased up to 16-fold as soon as any seeds were dispersed by the harvester. Given that uptake by the harvester is a function of phenology of seed production and dispersal, better data on such processes is required for weeds. Because rate of spread is more dependent on dispersal than on demographic factors, greater attention needs to be given to describing dispersal frequency distributions and especially to analysis of their shapes.

Targeting weed patches for site-specific herbicide applications potentially represents cost savings for operators, reduction in environmental herbicide effects, and increased efficiency of weed control. An experiment was initiated in a no-till corn field in Ontario, Canada, in 1998 and was continued in rotation with no-till soybeans in 1999. Weeds were intensively scouted, and distribution maps of the most common weeds (field horsetail, spiny sowthistle, dandelion, and common lambsquarters) were generated for both years. A prescription map for each plot was made using the weed density maps. Treatment decisions were based on a weed threshold value of 1 shoot m−2. Four herbicide treatments were compared: a conventional broadcast, a site-specific application targeting weed patches only, and two combinations of broadcast and site-specific applications. Treatments were applied using a direct-injection sprayer. Efficacy of weed control and yield were compared among treatments. In 1998 and 1999 there were no differences in the level of weed control or yield among treatments. The average percent area sprayed was reduced as much as 26% in the site-specific treatment in 1998 and up to 59% in the site-specific and broadcast combination treatments in 1999. For those species present in the field, patches ranged from highly aggregated to completely random, and patch stability ranged from very stable to very unstable over the 2 yr.

Synthetic seed banks are a useful tool for tracking how weed populations change over time. By sowing a known number of seeds of a given species within a quadrat with defined boundaries, an investigator can measure the number remaining and thereby calculate demographic rates (e.g., mortality). The alternative is to use in situ seeds and estimate their initial population density via sampling. To make a synthetic seed bank approach useful within an agricultural system subjected to soil disturbances such as tillage, one would need a way to account for seeds leaving the initial quadrat (i.e., a way to follow how the area encompassing the sown seeds changes over time). Without accounting for the change in location/extent of the synthetic seed bank, any field operation moving soil will create additional uncertainty in population size. Depending on the “aggressiveness” of specific field operations and the initial size of the quadrat, this effect might be negligible or so large as to be intractable. Here, we describe a method for following a synthetic seed bank over time using a “living boundary” of nondormant seeds, which effectively play the role of tracers used in the study of dynamics in other scientific disciplines. Study quadrats in East Lansing, MI, and Arlington, WI, were sown with giant foxtail and velvetleaf at a rate of 2,000 seeds m−2. The study quadrats were marked on the perimeter and diagonals using nondormant seeds of three marker species: kale, radish, and rye. The areas were then subjected to tillage and planting operations. Spatial coordinates of seedling locations for the marker and weed species were obtained through digital image processing. A nonparametric comparison of the spatial displacement of marker and weed species indicated that their empirical spatial distributions did not differ. The marker species quadrats described by the 50th, 90th, and 99th quantiles of movement contained all velvetleaf seedlings in Wisconsin, all velvetleaf seedlings in Michigan, and all giant foxtail seedlings in Michigan, respectively. The results suggest a simple rule for applying the method to field demography studies: after the original quadrat is deformed and seedlings have emerged, flag the polygon containing all marker seedlings to obtain the expanded quadrat containing the study weed population.

Recent work in regional science, geography, and urban economics has advanced spatial modeling of land markets and land use by incorporating greater spatial complexity, including multiple sources of spatial heterogeneity, multiple spatial scales, and spatial dynamics. Doing so has required a move away from relying solely on analytical models to partial or full reliance on computational methods that can account for these added features of spatial complexity. In the first part of the paper, we review economic models of urban land development that have incorporated greater spatial complexity, focusing on spatial simulation models with spatial endogenous feedbacks and multiple sources of spatial heterogeneity. The second part of the paper presents a spatial simulation model of exurban land development using an auction model to represent household bidding that extends the traditional Capozza and Helsley (1990) model of urban growth to account for spatial dynamics in the form of local land use spillovers and spatially heterogeneous land characteristics.

Patchy or divided populations can be important to infectious disease transmission. We first show that Lloyd’s mean crowding index, an index of patchiness from ecology, appears as a term in simple deterministic epidemic models of the SIR type. Using these models, we demonstrate that the rate of movement between patches is crucial for epidemic dynamics. In particular, there is a relationship between epidemic final size and epidemic duration in patchy habitats: controlling inter-patch movement will reduce epidemic duration, but also final size. This suggests that a strategy of quarantining infected areas during the initial phases of a virulent epidemic might reduce epidemic duration, but leave the population vulnerable to future epidemics by inhibiting the development of herd immunity.

Predatory beetles contribute to the control of crop pests and are an important food resource for farmland birds. Many of these beetle species overwinter as larvae within agricultural soils, however, their spatio-temporal emergence patterns are poorly understood, even though such knowledge can assist with their management for biocontrol. Soil moisture is considered to be a key factor influencing oviposition site selection and larval survival. The time, density and spatial pattern of Carabidae and Staphylidae emergence was therefore measured across two fields and compared to soil moisture levels in the previous winter and adult distribution in the previous July. The mean density of Carabidae and Staphylidae that emerged between April and harvest within each field was 157 and 86 m−2, indicating that soils are an important over-wintering habitat for beneficial invertebrates and should be managed sympathetically if numbers are to be increased. Of the species that were sufficiently numerous to allow their spatial pattern to be analysed, all showed a heterogeneous emergence pattern, although patches with high emergence were stable over the sampling period. The distribution of eight species was influenced by soil moisture levels in the previous winter and eight species, although not the same, were spatially associated with the distribution of adults in the previous summer suggesting that the females selected oviposition areas with the appropriate soil wetness.

A model is used to explore whether local density-dependent recruitment relationships can be observed when considering a larger scale. A virtual population of spawners is tracked within an artificial environment composed of cells. Spawners can move from one cell to another on a spatial grid defined as a square lattice (lattice scale) made of 20 × 20 jointed hexagonal cells (local scale). Five spawner's behaviours are experimented successively: i) spawners stay in the same cell to spawn; ii) they move randomly towards one of the neighbouring cells; iii) they move towards the least populated neighbouring cell; iv) they move towards the most populated neighbouring cell; and v) they move randomly towards a neighbouring cell and then move towards the most populated neighbouring cell. When the migration of spawners is achieved, spawners reproduce only once, recruitment takes place and then they disappear. The recruitment is an event which occurs at a local scale: at the scale of the cell. Using Ricker's stock-recruitment relationship, in each cell the number of recruits is a function of the spawners. Random migrations and migrations towards the less populated cell allow a homogeneous distribution of the spawners throughout the lattice. Whereas in the three other cases, this distribution is not homogenised. The homogenisation of the lattice allows synchrony between local populations and then a stock-recruitment relationship is observable at the lattice scale. Simulations show that local density-dependence is not always detectable when considering large spatial scale. This result strengthens the idea that the choice of spatial scale is essential when studying stock-recruitment relationship.